D.A. Rhoades | USGS Science

USGS2012

Probabilistic Relationships between Ground‐Motion Parameters and Modified Mercalli Intensity in California

We use a database of approximately 200,000 modified Mercalli intensity (MMI) observations of California earthquakes collected from USGS "Did You Feel It?" (DYFI) reports, along with a comparable number of peak ground-motion amplitudes from California seismic networks, to develop probabilistic relationships between MMI and peak ground velocity (PGV), peak ground acceleration (PGA), and 0.3-s, 1-s, and 3-s 5% damped pseudospectral acceleration (PSA). After associating each ground-motion observation with an MMI computed from all the DYFI responses within 2 km of the observation, we derived a joint probability distribution between MMI and ground motion. We then derived reversible relationships between MMI and each ground-motion parameter by using a total least squares regression to fit a bilinear function to the median of the stacked probability distributions. Among the relationships, the fit to peak ground velocity has the smallest errors, though linear combinations of PGA and PGV give nominally better results. We also find that magnitude and distance terms reduce the overall residuals and are justifiable on an information theoretic basis. For intensities MMI≥5, our results are in close agreement with the relations of Wald, Quitoriano, Heaton, and Kanamori (1999); for lower intensities, our results fall midway between Wald, Quitoriano, Heaton, and Kanamori (1999) and those of Atkinson and Kaka (2007). The earthquakes in the study ranged in magnitude from 3.0 to 7.3, and the distances ranged from less than a kilometer to about 400 km from the source.

California↗

USGS2007

A multiple-approach radiometric age estimate for the Rotoiti and Earthquake Flat eruptions, New Zealand, with implications for the MIS 4/3 boundary

Pyroclastic fall deposits of the paired Rotoiti and Earthquake Flat eruptions from the Taupo Volcanic Zone (New Zealand) combine to form a widespread isochronous horizon over much of northern New Zealand and the southwest Pacific. This horizon is important for correlating climatic and environmental changes during the Last Glacial period, but has been the subject of numerous disparate age estimates between 35.1±2.8 and 71±6 ka (all errors are 1 s.d.), obtained by a variety of techniques. A potassium–argon (K–Ar) age of 64±4 ka was previously determined on bracketing lavas at Mayor Island volcano, offshore from the Taupo Volcanic Zone. We present a new, more-precise 40 Ar/ 39 Ar age determination on a lava flow on Mayor Island, that shortly post-dates the Rotoiti/Earthquake Flat fall deposits, of 58.5±1.1 ka. This value, coupled with existing ages from underlying lavas, yield a new estimate for the age of the combined eruptions of 61.0±1.4 ka, which is consistent with U–Th disequilibrium model-age data for zircons from the Rotoiti deposits. Direct 40 Ar/ 39 Ar age determinations of plagioclase and biotite from the Rotoiti and Earthquake Flat eruption products yield variable values between 49.6±2.8 and 125.3±10.0 ka, with the scatter attributed to low radiogenic Ar yields, and/or alteration, and/or inheritance of xenocrystic material with inherited Ar. Rotoiti/Earthquake Flat fall deposits occur in New Zealand in association with palynological indicators of mild climate, attributed to Marine Isotope Stage (MIS) 3 and thus used to suggest an age that is post-59 ka. The natures of the criteria used to define the MIS 4/3 boundary in the Northern and Southern hemispheres, however, imply that the new 61 ka age for the Rotoiti/Earthquake Flat eruption deposits will provide the inverse, namely, a more accurate isochronous marker for correlating diverse changes across the MIS 4/3 boundary in the southwest Pacific.

Quaternary Science Reviews↗

USGS2007

Earthquake likelihood model testing

INTRODUCTION The Regional Earthquake Likelihood Models (RELM) project aims to produce and evaluate alternate models of earthquake potential (probability per unit volume, magnitude, and time) for California. Based on differing assumptions, these models are produced to test the validity of their assumptions and to explore which models should be incorporated in seismic hazard and risk evaluation. Tests based on physical and geological criteria are useful but we focus on statistical methods using future earthquake catalog data only. We envision two evaluations: a test of consistency with observed data and a comparison of all pairs of models for relative consistency. Both tests are based on the likelihood method, and both are fully prospective ( i.e. , the models are not adjusted to fit the test data). To be tested, each model must assign a probability to any possible event within a specified region of space, time, and magnitude. For our tests the models must use a common format: earthquake rates in specified “bins” with location, magnitude, time, and focal mechanism limits. Seismology cannot yet deterministically predict individual earthquakes; however, it should seek the best possible models for forecasting earthquake occurrence. This paper describes the statistical rules of an experiment to examine and test earthquake forecasts. The primary purposes of the tests described below are to evaluate physical models for earthquakes, assure that source models used in seismic hazard and risk studies are consistent with earthquake data, and provide quantitative measures by which models can be assigned weights in a consensus model or be judged as suitable for particular regions. In this paper we develop a statistical method for testing earthquake likelihood models. A companion paper ( Schorlemmer and Gerstenberger 2007 , this issue) discusses the actual implementation of these tests in the framework of the RELM initiative. Statistical testing of hypotheses is a common task and a wide range of possible testing procedures exist. Jolliffe and Stephenson ( 2003 ) present different forecast verifications from atmospheric science, among them likelihood testing of probability forecasts and testing the occurrence of binary events. Testing binary events requires that for each forecasted event, the spatial, temporal and magnitude limits be given. Although major earthquakes can be considered binary events, the models within the RELM project express their forecasts on a spatial grid and in 0.1 magnitude units; thus the results are a distribution of rates over space and magnitude. These forecasts can be tested with likelihood tests. In general, likelihood tests assume a valid null hypothesis against which a given hypothesis is tested. The outcome is either a rejection of the null hypothesis in favor of the test hypothesis or a nonrejection, meaning the test hypothesis cannot outperform the null hypothesis at a given significance level. Within RELM, there is no accepted null hypothesis and thus the likelihood test needs to be expanded to allow comparable testing of equipollent hypotheses. To test models against one another, we require that forecasts are expressed in a standard format: the average rate of earthquake occurrence within pre-specified limits of hypocentral latitude, longitude, depth, magnitude, time period, and focal mechanisms. Focal mechanisms should either be described as the inclination of P -axis, declination of P -axis, and inclination of the T -axis, or as strike, dip, and rake angles. Schorlemmer and Gerstenberger ( 2007 , this issue) designed classes of these parameters such that similar models will be tested against each other. These classes make the forecasts comparable between models. Additionally, we are limited to testing only what is precisely defined and consistently reported in earthquake catalogs. Therefore it is currently not possible to test such information as fault rupture length or area, asperity location, etc. Also, to account for data quality issues, we allow for location and magnitude uncertainties as well as the probability that an event is dependent on another event. As we mentioned above, only models with comparable forecasts can be tested against each other. Our current tests are designed to examine grid-based models. This requires that any fault-based model be adapted to a grid before testing is possible. While this is a limitation of the testing, it is an inherent difficulty in any such comparative testing. Please refer to appendix B for a statistical evaluation of the application of the Poisson hypothesis to fault-based models. The testing suite we present consists of three different tests: L-Test, N-Test, and R-Test. These tests are defined similarily to Kagan and Jackson ( 1995 ). The first two tests examine the consistency of the hypotheses with the observations while the last test compares the spatial performances of the models.

Seismological Research Letters↗